## Closer to Erdös…

After one of my lectures a year or so ago, a student came up to me and asked whether I had an Erdős number** **and, if so, what it was. I didn’t actually know** **what he was talking about but tried to find out and eventually posted about it.

In case you didn’t know, Paul Erdős (who died in 1996) was an eccentric Hungarian mathematician who wrote more than 1000 mathematical papers during his life but never settled in one place for any length of time. He travelled between colleagues and conference, mostly living out of a suitcase, and showed no interest at all in property or possessions. His story is a fascinating one, and his contributions to mathematics were immense and wide-ranging. The Erdős number is a tiny part of his legacy, but one that seems to have taken hold. Some mathematicians appear to take it very seriously, but most treat it with tongue firmly in cheek, as I certainly do.

So what is the Erdős number?

It’s actually quite simple to define. First, Erdős himself is assigned an Erdős number of zero. Anyone who co-authored a paper with Erdős has an Erdős number of 1. Then anyone who wrote a paper with someone who wrote a paper with Erdős has an Erdős number of 2, and so on. The Erdős number is thus a measure of “collaborative distance”, with lower numbers representing closer connections.

I say it’s quite easy to define, but it’s rather harder to calculate. Or it would be were it not for modern bibliographic databases. In fact there’s a website run by the American Mathematical Society which allows you to calculate your Erdős number as well as a similar measure of collaborative distance with respect to any other mathematician.

A list of individuals with very low Erdős numbers (1, 2 or 3) can be found here.

Given that Erdős was basically a pure mathematician, I didn’t expect first to show up as having any Erdős number at all, since I’m not really a mathematician and I’m certainly not very pure. However, his influence is clearly felt very strongly in physics and a surprisingly large number of physicists (and astronomers) have a surprisingly small Erdős number.

Anyway, my erstwhile PhD supervisor John D. Barrow recently emailed to point out that he had written a paper with Robin Wilson, who once co-authored a paper (on graph theory) with Erdős himself. That means John’s Erdős number is now 2, mine is consequently no higher than 3, and anyone I’ve ever written a paper with now has an Erdős number no greater than 4.

I’ll be making sure this new information is included in our forthcoming REF submission.

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This entry was posted on December 18, 2011 at 9:08 am and is filed under Biographical with tags Erdos Number, John D. Barrow, Mathematicians, mathematics, Paul Erdos. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

December 18, 2011 at 9:19 am

Apparently Kevin Bacon has an Erdős number of 5 (or is that degrees of seperation ?)

December 19, 2011 at 12:14 pm

Looks like mine is 5. Wow !

Starting off in Elec. Engineering at Cardiff: Me – Prof. AJ Moses – Prof. JE Thompson – HF Sandham*- MS Klamkin* – Erdos*

(*=mathematician)

Sandham is the link-man into mathematics. Providing there are not two HF Sandham’s authoring in 1960, the above proposition is true. I am conditionally chuffed.

Check http://www.oakland.edu/enp/thedata/ for list of people with Erdos <= 2.

December 18, 2011 at 9:22 am

I wrote a paper with Ian Smail, who wrote a paper with George Djorgovski, who wrote a paper with Jogesh Babu, who wrote a paper with Paul Erdös, so my Erdös number is no more than four. This is four less than Erwin Schrödinger. There’s a lesson in there somewhere but for some reason I don’t feel it’s in my best interests to point it out.

December 18, 2011 at 9:26 am

Max Tegmark apparently wrote a paper with his father, Harold Shapiro, who wrote a paper with Erdos. So my Erdos number is also 3. Best chance for cosmologists for a low Erdos-Bacon number (Bacon number being similarly defined for links to actor Kevin Bacon through films) may be through Ravi Sheth, who appeared as Kim in the film of the same name when he was about 15. Clearly the lure of a life of fame and adulation by adoring fans was too great, as he chose the life of an academic rather than a film star. Does anyone know his Bacon number?

December 18, 2011 at 10:02 am

Someone pointed out to me after my previous post on this subject that your number was 3 which meant mine had already reduced from the 5 I calculated in that post to 4, as we have co-authored papers in the past year.

December 18, 2011 at 12:41 pm

ps. I once appeared in a TV programme with Sam Neill, but I think that probably doesn’t count.

December 18, 2011 at 3:08 pm

I had no idea about Ravi’s cinematic past. The only Bacon number calculator I know about, http://oracleofbacon.org/ , doesn’t want to count KIm, probably because it was a TV movie. But Peter O’Toole, who was in Kim, has a Bacon number of 2, so Ravi’s is at most 3 if you allow TV movies.

And Ravi’s on a number of papers with Max Tegmark, so his Erdos number is presumably also 3.

After working this out myself, I find that Wikipedia already knows the answer: “Astrophysicist and cosmologist Ravi Sheth at the University of Pennsylvania also has an Erdős–Bacon number of at most 6.” (http://en.wikipedia.org/wiki/Erdős–Bacon_number)

December 19, 2011 at 8:50 am

I’ve often wondered whether Max wrote that paper primarily to decrease his Erdős number. 🙂

I also have an Erdös number of at most 4, there being multiple paths to both Djorgovski and Tegmark. I suspect that most cosmologists with low Erdős numbers go through Djorgovski or Tegmark (or both), though Barrow of course is another possibility.

I must remember to buy Max a beer the next time I see him. 🙂

Note that among fans of Fairport Convention, there is the concept of the Pegg number.

Actually, considering the idea of 6 degrees of separation, we shouldn’t be that surprised at relatively low Erdős numbers. A while back over at the e-Astronomer, those not convinced of the ubiquity of this phenomenon challenged us believers to come up with a link between me and the president of an African nation. Of course, I wasn’t surprised that I came up with one quickly, but then someone I don’t know (but might have met briefly) came up with a completely different path in a very short time.

December 19, 2011 at 9:05 am

http://andyxl.wordpress.com/2010/05/04/six-degrees-of-twitter/

December 18, 2011 at 3:54 pm

So Peter, our 1990s paper attacking the Copenhagen interpretation, frequentist probability, wrong interpretations of the anthropic principle and the claim that the moon is made of green cheese gives me an Erdös number not exceeding 4. I would never have guessed. Why not put yourself into that Wikipedia page as a threesie?

Good to see that Janos Aczel is a 1; the great man of functional equations – lovely subtle things and as far from being soluble by computer algebra, relative to differential equations, as Go is from chess.

December 18, 2011 at 6:28 pm

Good idea! (And now done….)

That reminded me also as an act of seasonal goodwill to make a donation to wikipedia….I hope readers of this blog will consider doing likewise.

December 19, 2011 at 1:41 pm

Hmm, well that would give me another route to a number of 5 (via my PhD supervisor, Jirina Stone, who as coauthored with Joseph Silk, who has coauthored with John Barrow ( instead of the route at http://personal.ph.surrey.ac.uk/~phs3ps/erdos.html ).

I guess I have a Bacon number of 3, if you count TV, and not film appearances, following my possibly ill-advised agreement to be a scientific “expert” in an episode of William Shatner’s Weird or What.

I guess the whole point is that pretty much everyone, no matter how lowly, has such a number.

December 22, 2011 at 8:41 am

Actually, it’s the interesting case of being either relatively small or being infinite.

January 2, 2012 at 7:43 pm

I’m John’s newest PhD student. I had no idea his Erdős number so recently shrank. Thanks for the heads up! 🙂